Conformational Study of 1,2-Cycloundecadiene by Dynamic NMR Spectroscopy and Computational Methods Judge Brown, II, Diwakar M. Pawar, and Eric A. Noe* Department of Chemistry, Jackson State University, Jackson, Mississippi 39217-0510
[email protected] Received May 6, 2002
Solutions of 1,2-cycloundecadiene in propane were studied by low-temperature 13C NMR spectroscopy. A total of 17 peaks were observed at -166.7 °C, corresponding to two conformations of similar populations, one of C1 symmetry (11 peaks) and the other of C2 symmetry. The line shapes show that the predominant pathway for exchange of the topomers (C1 and C1′) of the C1 conformation does not include the C2 conformation. From the 13C spectra, free-energy barriers of 8.38 ( 0.15, 9.45 ( 0.15, and 9.35 ( 0.15 kcal/mol were determined for the C1 to C1′, (C1 + C1′) to C2, and C2 to (C1 + C1′) conversions, respectively, at -72.2 °C. The NMR results for this compound are discussed in terms of the conformations predicted by molecular mechanics calculations obtained with Allinger’s MM3 program. Ab initio calculations of free energies are also reported at the HF/ 6-311G* level for 25 conformations. Introduction A combination of dynamic NMR spectroscopy and computational methods provides a useful way of studying the conformations of cyclic compounds. The structures of the possible stable conformations and their energies and symmetries can be obtained from the calculations; in favorable cases, dynamic NMR spectroscopy shows the number of conformations actually present at low temperatures, their relative free energies and populations, symmetries, and free-energy barriers to interconversion. The two CH2 groups of allene are perpendicular to each other, and the 2-fold rotational axis perpendicular to the CdCdC axis of this compound can be maintained in cyclic allenes1 such as 1,2-cycloundecadiene, which would show six peaks in the low-temperature 13C NMR spectra for each conformation of C2 or time-averaged C2 symmetry, and 11 peaks for each conformation of C1 symmetry. We report here a conformational study of 1,2cycloundecadiene by dynamic NMR spectroscopy and molecular mechanics and ab initio calculations.
Experimental Section 1,2-Cycloundecadiene (1)5 was synthesized from cis- and trans-cyclodecenes by a procedure similar to the one described by Shea and Kim6 for the synthesis of 1,2-cyclononadiene from cyclooctene.7 Twenty grams of a 3:1 mixture of cis- and transcyclodecenes was added to 1.5 mL of ethanol, 73.1 g of * To whom correspondence should be addressed. Fax: 601-979-3674. (1) 1,2-Cyclononadiene has been studied by several methods2-4 and exists as a mixture of a C2 and a C1 conformation. (2) Allinger, N. L.; Pathiaseril, A. J. Comput. Chem. 1987, 8, 1225. (3) Traetteberg, M.; Bakken, P.; Almenningen, A. J. Mol. Struct. 1981, 70, 287. (4) Anet, F. A. L.; Yavari, I. J. Am. Chem. Soc. 1977, 99, 7640. (5) Moore, W. R.; Ward, H. R. J. Am. Chem. Soc. 1962, 27, 4179. (6) Shea, K. J.; Kim, J.-S. J. Am. Chem. Soc. 1992, 114, 3044. (7) Gardner, P. D.; Narayana, M. J. Org. Chem. 1961, 26, 3518.
bromoform, 29 mL of dichloromethane, 0.363 g of benzyltriethylammonium chloride, and 115.8 g of aqueous 50% sodium hydroxide solution, and the mixture was heated to 40-50 °C for 2 h with vigorous stirring, followed by stirring for 2 h at room temperature. Examination of the organic phase by 13C NMR spectoscopy showed the presence of some unreacted cyclodecenes; additional bromoform, ethanol, benzyltriethylammonium chloride, and 50% sodium hydroxide were added, and the mixture was stirred vigorously at 40-50 °C for 2 h and stirred 2 h at room temperature. Water was added, and the dichloromethane layer was removed. The aqueous phase was extracted three times with dichloromethane, and the combined organic layers were washed with 5% hydrochloric acid and then water, dried over Drierite, and the solvent was evaporated. Excess bromoform was removed by heating under vacuum to yield 44.9 g of a cis- and trans-11,11-dibromobicyclo[8.1.0]undecane mixture. A 13C NMR spectrum indicated a high level of purity (>98%) for the residue. One or both of the gem-bromocyclopropanes precipitated at -30 to -40 °C from a solution of 38.1 g of the dibromides in 19.1 mL of ether; an additional 10 mL of ether was added, and the temperature was raised to -2 to -5 °C while methyllithium (10 mL of a 1.4 M solution in ether) was added dropwise under argon with stirring. An additional 95.4 mL of methyllithium was added as the temperature was gradually decreased until a temperature of -30 to -40 °C was reached and maintained. After the addition was completed, the resulting solution was stirred at -30 to -40 °C for 1 h. The excess methyllithium was decomposed by adding water, and the reaction mixture was extracted with ether. The combined ether layers were washed with water, dried over Drierite, and concentrated on the rotary evaporator. Distillation under vacuum gave 12.7 g of 1, 2 -cycloundecadiene; the product was identified by its 13C spectrum, which also established a high level of purity (g99%). A 30% solution of 1 in propane was prepared in a 5 mm thin-walled NMR tube and used to record 13C spectra from room temperature to -90.0 °C. For lower temperatures, a 2% solution was used. A small amount of TMS was added as an internal reference to both solutions. Caution: high pressure. The sample tubes were stored and handled below 0 °C most of the time. Spectra were recorded on a General Electric Model 10.1021/jo020317c CCC: $25.00 © 2003 American Chemical Society
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Published on Web 03/28/2003
Conformational Study of 1,2-Cycloundecadiene GN-300 wide-bore NMR spectrometer operating at 75.58 MHz for carbon. The 13C spectra for 1 were obtained from +17.8 to -166.3 °C with a 5 mm dual probe. A pulse width of 8.0 µs, corresponding to a tip angle of 83°, was used. The pulse repetition period was 10 s at -166.3 °C, and 1 s at all other temperatures. A sweep width of (9600 Hz, data size of 32 K, 800-1200 pulses, and 3.0 Hz line broadening were used. Spinning was discontinued below about -120 °C. Because ejecting the sample at the lower temperatures was difficult, due to ice formation on the inner wall of the stack, the temperature calibrations were performed separately, using a copper-constantan thermocouple immersed in the same solvent contained in a nonspinning dummy sample tube and under conditions as nearly identical as possible. The emf’s were measured with a Leeds and Northrup Model 8690-2 millivolt potentiometer. The uncertainty in the temperatures was estimated to be (2 °C. The rate constants for the interconversion of conformations from the carbon spectra were obtained by total line shape matching on a PC using a DNMR simulation program,8 and the free-energy barriers were obtained on an Apple computer with a program written by Newmark.9 The conformational space of 1 was searched with Allinger’s MM3 program.10 Kick sizes of 2.0 and 3.0 Å and several different numbers of pushes were used, and the results were combined. The conformations were visualized with Spartan 5.0.11 The geometries determined by the molecular mechanics program for the first 25 conformations of 1 according to strain energy were used as starting points for the ab initio calculations. The Gaussian 94 series of programs12 was used for full geometry optimization, first at the HF/3-21G* level and then at the HF/6-311G* level. The optimized geometries were tested by frequency calculations, and free energies were obtained for -150 °C.
Results and Discussion The 13C spectrum of 1 at -25.0 °C shows the expected six signals at δ 204.13 (dCd), 93.71 (dCH), 29.61, 28.90, 26.18, and 24.68, relative to the carbons of internal TMS (Figure 1). A small amount of exchange broadening is apparent at this temperature, as indicated by the decreased height for two of the peaks in the CH2 region. Further changes occur at lower temperatures, and by -166.3 °C, two peaks were found in the dCd region, which shows the presence of two conformations of similar populations. The spectrum for the dCH carbons at this temperature consists of three peaks, two of which are of equal intensity and correspond to a conformation of C1 symmetry (1A). The third peak in this region is assigned (8) Calculated spectra were obtained using program DNMR-SIM written by Hagele, G., Fuhler, R., Heinrich-Heine University, Dusseldorf Institute of Inorganic and Structural Chemistry, Dusseldorf, FRG, 1994. (9) Free-energy barriers were calculated from the Eyring equation with a program written by Newmark: Newmark, R. A. J. Chem. Educ. 1983, 60, 45. (10) ) Version MM3 (2000) was used. This latest version of the MM3 program is available to academic users from the Quantum Chemistry Program Exchange and to commercial users from Tripose Associates, 1699 South Hanley St., St. Louis, MO 63144. (11) Spartan version 5.10 from Wavefunction, Inc., Irvine, CA. (12) Gaussian 94, Revision E.3: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian, Inc., Pittsburgh, PA, 1995.
FIGURE 1. Low-temperature
13C
NMR spectra of 1,2-cy-
cloundecadiene (1) in propane.
to a conformation of C2 (or time averaged C2) symmetry (1B). The line shapes for the dCd and dCH regions at temperatures near -72.2 °C indicate that the highfrequency signal at -166.3 °C for the former region corresponds to the conformation of C1 symmetry. The peaks for the C1 conformation at -166.3 °C appear at δ 204.29, 94.21, 90.40, 34.21, 29.77, 28.46, 27.98, 26.79, 25.45, 24.72, and 24.23; the peaks at δ 201.50, 96.23, 31.41, 28.83, 24.01, and 19.91 were assigned to the C2 conformation. The line shapes for the dCH carbons at temperatures below -72.2 °C indicate that interconversion of the
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Brown et al. TABLE 1. Actual Temperatures, Populations, Rate Constants for Interconversions, and Free-Energy Barriers for 1,2-Cycloundecadiene T (°C)
pop. C1 + C1′
-67.9 -72.2 -80.6 -90.0 -166.3
0.590 0.568 0.550 0.525 0.465
k1 (s-1) rate C1 f C1′
k2 (s-1) rate C1 f C2
k3 (s-1) rate C2 f C 1
2k3 (s-1) rate C2 f (C1 + C1′)
∆Gq C1 f C1′
∆Gq (C1 + C1′) f C2
∆Gq C2 f (C1 + C1′)
4200 3140 910 480
483 215 115 35
348 141 70.3 19.3
696 282 141 38.6
8.45 8.38 8.49 8.29
9.34 9.45 9.28 9.24
9.19 9.35 9.20 9.21
FIGURE 2. Experimental and calculated line shapes for the dCd carbons of 1,2-cycloundecadiene (1) at four temperatures.
topomers 13,14 of 1A takes place predominantly (but not entirely) by a pathway that does not include 1B. Calculated line shapes were based on the exchange scheme shown above, where C1 and C1′ are the two topomers of 1A. From line shape matching of the dCd region, k2 and 2k3 could be obtained, and these rate constants were used in the calculation of line shapes for the dCH region, along with values for k1, which were determined from the latter calculations. Calculated and experimental line shapes for four temperatures are shown in Figures 2 and 3, and the rate constants and free-energy barriers are summarized in Table 1. For example, the populations of C1, C1′, and C2 at -72.2 °C were 0.284, 0.284, and 0.432 and k2 and k3 were 215 and 141 s-1; the free-energy barrier for conversion of (C1 + C1′) to C2 was calculated from the rate constant of 215 s-1 to be 9.45 kcal/mol, and the rate constant and free-energy barrier for the reverse process were 282 s-1 and 9.35 kcal/mol. As expected, k1 is much higher (3140 s-1 at -72.2 °C) than k2 and k3 ; the freeenergy barrier for interconversion of C1 and C1′ was 8.38 kcal/mol. (13) Eliel, E. L.; Wilen, S. H. Sterochemistry of Organic Compounds; Wiley-Interscience: New York, 1994; p 506. (14) Binsch, G.; Eliel, E. L.; Kessler, H. Angew. Chem., Inter. Ed. Engl. 1971, 10, 570.
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FIGURE 3. Experimental and calculated line shapes for the dCH carbons of 1,2-cycloundecadiene at four temperatures.
Structures calculated at the HF/6-311G* level for the first 10 conformations of 1 according to MM3 strain energies are shown in Figure 4. The symmetries and calculated strain energies and free energies according to MM3 for the 25 most stable conformations according to strain energy are listed in Table 2, and relative free energies from ab initio calculations at the HF/6-311G* level are also included. After optimization at the HF/ 6-311G* level, conformations 1g and 1h converged to a structure that closely resembled 1g. Conformations 1x and 1y converged to the enantiomer of 1a. 1,3-Symmetrically disubstituted allenes are chiral, and the enantiomers can be interconverted by rotation about the double bonds, but the barriers for this process are high. From the rate of racemization of 1,3-dimethylallene, the rotational barrier of the CdC bonds was determined15 to be 46.17 kcal/mol for this compound. The dihedral angles from MM3 and ab initio calculations are generally close for most of the conformations of Figure 4, except for C11C1C2C3 and C1C2C3C4, which are often very different. These dihedral angles depend on small distortions of the C1C2C3 group from linearity, so perhaps the deviations are not surprising. The C1C2C3 (15) Roth, W. R.; Ruf, G.; Ford, P. W. Chem. Ber. 1974, 107, 48.
Conformational Study of 1,2-Cycloundecadiene
FIGURE 4. Conformations of 1,2-cycloundecadiene (1) in order of increasing MM3 strain energies. The numbers refer to CCCC dihedral angles. The values on top in parentheses are from MM3 and the lower numbers are from ab initio calculations at the HF/6-311G* level (used for the drawings).
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Brown et al. TABLE 2. Relative Strain Energiesa and Relative Free Energiesa Calculated Using the Molecular Mechanics Force Field (MM3) and Relative Free Energiesb and Low Frequenciesb for Different Conformations of 1,2-Cycloundecadiene Calculated at the HF/6-311G* Level Using the Gaussian 94 Program
conformer
symmetry
relative strain energies (kcal/mol)
1a 1b 1c 1d 1e 1f 1g 1h 1i 1j 1k 1l 1m 1n 1o 1p 1q 1r 1s 1t 1u 1v 1w 1x 1y
C1 C1 C1 C1 C2 C1 C2 C2 C1 C2 C1 C1 C1 C1 C1 C1 C1 C1 C2 C1 C1 C1 C2 C1 C1
0.000 0.402 0.620 1.215 1.626 2.002 2.155 2.279 2.348 2.364 2.378 2.383 2.445 2.447 2.479 2.800 3.142 3.206 3.531 3.557 3.773 3.816 4.168 4.271 4.273
relative free energiesa (kcal/mol) 25 °C -166.3 °C
relative free energiesb (kcal/mol) 25 °C -166.3 °C
0.000 0.579 0.512 1.320 2.222 2.134 1.935 2.284 2.373 2.290 2.503 2.647 3.687 2.362 2.386 3.094 2.992 3.210 3.352 4.137 4.042 3.759 4.940 4.444 4.446
0.000 1.212 1.351 1.999 0.217 1.306 3.219 3.219 3.890 2.679 2.132 3.889 4.898 2.882 2.859 3.106 4.745 4.086 2.457 5.340 6.019 3.333 4.204 0.001 0.000
0.000 0.473 0.512 1.367 2.177 2.249 1.893 2.334 2.327 2.185 2.673 2.668 3.429 2.506 2.486 3.210 2.975 3.243 3.329 3.948 3.959 3.864 3.708 3.928 3.930
0.000 1.168 1.440 2.169 0.265 1.426 3.547 3.547 3.899 2.871 2.272 3.901 4.749 3.094 3.030 3.222 5.092 4.242 2.574 5.201 6.092 3.491 4.251 0.000 0.000
low frequenciesb (cm-1) 84.9256 87.9764 69.8268 54.4559 92.2170 80.4187 38.4844 38.4846 107.5399 86.9023 78.1287 80.7804 107.7798 65.7568 73.2783 76.0551 50.9557 55.1516 93.0544 113.3284 81.0494 87.0930 109.2182 84.9593 84.9257
conformations 1A and 1B. Another view of these conformations is shown on the left. Several conformations (1b, 1c, and 1f) are close enough in free energy that they cannot be completely excluded.
Acknowledgment. We thank the National Science Foundation (NSF-CREST Grant No. HRD-9805465) for support of this work and the Mississippi Center for Supercomputing Research for a generous amount of time. Some of the calculations were done using the molecular modeling laboratory at Jackson State University supported by the Army High Performance Computing Research Center.
bond angles for conformations 1a-j are close to 180°, as expected (179.3, 179.4, 177.9, 176.9, 177.8, 179.4, 173.9, 173.9, 178.3, and 180.0°, respectively), and the corresponding C11C1C3C4 dihedral angles for these conformations are not far from 90° (93.9, -84.2, -87.0, -90.8, 96.5, 93.3, -79.4, -79.4, -83.8, and 91.9°). On the basis of the ab initio calculations, the most likely structures are 1a and 1e for the C1 and C2
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Supporting Information Available: The Cartesian coordinates and calculated energies for the 25 conformations of 1,2-cycloundecadiene at the HF/6-311G* level (Table 2) are provided. Cartesian coordinates for these conformations obtained with the MM3 force field and dihedral angles for conformations 1k-y at the HF/6-311G* level are also included. This material is available free of charge via the Internet at http://pubs.acs.org. JO020317C
